def abc_hit(N):
"""Yield all abc-hits with c < N."""
r = rad(N)
for a in xrange(1, (N - 1) / 2 + 1):
if a % 100 == 0:
print "a", a
for b in xrange(a + 1, N - a):
c = a + b
rab = r[a] * r[b]
if rab < c and rab * r[c] < c and gcd(a, b) == 1:
yield a, b, c
def is_unique_perimeter(s):
if s % 100000 == 0: print s
s2, count = s / 2, 0
for m in ifilter(lambda m: s2 % m == 0, xrange(2, int(ceil(s2 ** 0.5)))):
sm = s2 / m # s/(2m), need to find odd factor k of
while sm % 2 == 0: sm /= 2 # Reduce search space of odd factors kby removing all 2-factors
for k in xrange(m + 1 + (m % 2), min(2 * m, sm + 1), 2):
if sm % k == 0 and gcd(k, m) == 1:
d, n = s2 / (k * m), k - m
m2, n2 = m * m, n * n
a, b = d * (m2 - n2), 2 * d * m * n
if a > b: a, b = b, a
count += 1
if count == 1: a1, b1 = a, b
elif count == 2 and a == a1 and b == b1: return False
return count == 1
# count += 1
# print 'f[%d,%d,%d] = %d' % (m, n, i, count)
# return count
#
# g = lambda k, S: sum(f(k, k - 1, i, S) for i in xrange(k)) + sum(f(k, k, i, S) for i in xrange(k + 1))
#
# def num_triangles(N):
# S, G = squares_dict(N), 0
# for n in xrange(1, N + 1):
# gn = g(n, S)
# G += gn
# print 'n', n, 'g[n]', gn, 'S[n]', n * n + G
# yield n * n + G
#
# if __name__ == "__main__":
# N = 2
# print [(a * a + b * b, (a, b)) for a, b in it.product(xrange(2 * N + 1), xrange(2 * N + 1))]
# S = squares_dict(N)
# print f(2, 2, 2, S)
# print list(num_triangles(2)) # [-1]
from euler.problem005 import gcd
num_triangles = lambda n: 3 * n * n + 2 * sum(
min(y * f / x, (n - x) * f / y)
for x, y, f in ((x, y, gcd(x, y)) for x in xrange(1, n + 1) for y in xrange(1, n + 1))
)
if __name__ == "__main__":
print num_triangles(50)
def prog_sq2(N):
'''Return the set of progressive perfect squares <= N.'''
result = set([])
for a in xrange(2, int((N - 1) ** (1. / 3.)) + 1):
a3 = a ** 3
for b in (b for b in xrange(1, min(a, int(0.5 * ((a3 * a3 + 4 * N) ** 0.5 - a3)) + 1)) if gcd(a, b) == 1):
ab, b2 = a3 * b, b * b
for k in xrange(1, int((b ** 4 + 4 * N * ab) ** 0.5 - b2) / (2 * ab) + 1):
n = k * (k * ab + b2)
if int(n ** 0.5) ** 2 == n:
print 'n', '=', int(n ** 0.5), '^ 2'
result.add(n)
return result
T = lambda n: sum(gcd_steps(n, m) for m in xrange(n))
tau_restricted = lambda n, r: sum(k for d, k in (gcd_and_steps(m, n) for m in xrange(r)) if d == 1) # @UnusedVariable
tau = lambda n: tau_restricted(n, n)
if __name__ == "__main__":
N = 100
print S(N), 2 * sum(T(n) for n in xrange(1, N + 1)) + N * (N + 1) / 2
print gcd_steps(47, 13)
print gcd_steps(8, 13)
d = 24
p = 3
print tau(p * d), sum(gcd_steps(i + k * d, p * d) for i in xrange(d) for k in xrange(p) if gcd(i, d) == 1)
for i in (i for i in xrange(d) if gcd(d, i) == 1):
print 'i %3d' % i,
for k in xrange(p):
print (i + k * d, p * d), gcd_steps(i + k * d, p * d),
# if k == 0:
# print (i, p * d),
# elif k == (p - 1) / 2:
# if i > d / 2:
# print (d * p - i - k * d, p * d), 1,
# else:
# print (i + k * d, p * d),
# elif k > p / 2:
# print (d * p - i - k * d, p * d), 1,
# else: